Cooled muon beams are essential to enable future Neutrino Factory and Muon Collider facilities. The international Muon Ionization Cooling Experiment (MICE) aims to demonstrate muon beam cooling through ionization energy loss in material. A figure of merit for muon beam cooling in MICE is the transverse root-mean-square (RMS) emittance reduction and to measure this, the individual muon positions and momenta are reconstructed using two scintillating-fiber tracking detectors housed in spectrometer solenoid modules. The reconstructed positions and momenta before and after a low-Z absorbing material are then used for constructing the covariance matrix and measuring normalized transverse RMS emittance of MICE muon beam. However, RMS emittance is sensitive to nonlinear effects in beam optics. In this study, the direct measurement of phase-space density as an alternative approach to measuring the muon beam cooling using the novel Kernel Density Estimation (KDE) method, is described.